This is Dr. David
these are the different stages of kidney disease:
Stage 1 with normal or high GFR (GFR > 90 mL/min)
Stage 2 Mild CKD (GFR = 60-89 mL/min)
Stage 3A Moderate CKD (GFR = 45-59 mL/min)
Stage 3B Moderate CKD (GFR = 30-44 mL/min)
Stage 4 Severe CKD (GFR = 15-29 mL/min)
Stage 5 End Stage CKD (GFR <15 mL/min)
your GFR most likely is an eGFR which is an estimated GFR which is estimated from your age and creatinine level and sex and race.
to get a true GFR level, you need a 24 hour urine collection study to get a clear picture of your kidney function and true GFR and true creatinine clearance numbers
it doesn't sound like you have had a 24 hour urine collection yet.
that is why your second doctor thinks your kidneys are probably better than an estimated GFR of 51.
let me know if you have questions.